AxisKeys.jl
This package defines a thin wrapper which, alongside any array, stores a vector of "keys"
for each dimension. This may be useful to store perhaps actual times of measurements,
or some strings labeling columns, etc. These will be propagated through many
operations on arrays (including broadcasting, map
, comprehensions, sum
etc.)
and altered by a few (sorting, fft
, push!
).
It works closely with NamedDims.jl, another wrapper
which attaches names to dimensions. These names are a tuple of symbols, like those of
a NamedTuple
, and can be used for specifying which dimensions to sum over, etc.
A nested pair of these wrappers can be made as follows:
using AxisKeys
data = rand(Int8, 2,10,3) .> abs;
A = KeyedArray(data; channel=[:left, :right], time=range(13, step=2.5, length=10), iter=31:33)
Selections
Indexing still works directly on the underlying array,
and keyword indexing (of a nested pair) works exactly as for a NamedDimsArray
.
But in addition, it is possible to pick out elements based on the keys,
which for clarity I will call lookup. This is written with round brackets:
Dimension d 
Indexing: i โ axes(A,d) 
Lookup: key โ axiskeys(A,d) 

by position  A[1,2,:] 
A(:left, 15.5, :) 
by name  A[iter=1] 
A(iter=31) 
by type    B = A(:left) 
When using dimension names, fixing only some of them will return a slice,
such as B = A[channel=1]
.
You may also give just one key, provided its type matches those of just one dimension,
such as B = A(:left)
where the key is a Symbol.
There are also a numer of special selectors, which work like this:
Indexing  Lookup  

one nearest  B[time = 3] 
B(time = Near(17.0)) 
vector 
all in a range  B[2:5, :] 
B(Interval(14,25), :) 
matrix 
all matching  B[3:end, Not(3)] 
B(>(17), !=(33)) 
matrix 
mixture  B[1, Key(33)] 
B(Index[1], 33) 
scalar 
nonscalar  B[iter=[1, 3]] 
B(iter=[31, 33]) 
matrix 
Here Interval(13,18)
can also be written 13..18
, it's from IntervalSets.jl.
Any functions can be used to select keys, including lambdas: B(time = t > 0<t<17)
.
You may give just one ::Base.Fix2
function
(such as <=(18)
or ==(20)
) provided its argument type matches the keys of one dimension.
An interval or a function always selects via findall
,
i.e. it does not drop a dimension, even if there is exactly one match.
While this table shows lookup selectors inside B(...)
, they can in fact all be
used inside B[...]
, not just Key(k)
as shown. They still refer to keys not indices!
(This will not select dimension based on type, i.e. A[Key(:left)]
is an error.)
You may also write Index[end]
but not Index[end1]
.
By default lookup returns a view, while indexing returns a copy unless you add @views
.
This means that you can write into the array with B(time = <=(18)) .= 0
.
For scalar output, you cannot of course write B(13.0, 33) = 0
as this parsed as a function definition, but you can write B[Key(13.0), Key(33)] = 0
,
or else B(13.0, 33, :) .= 0
as a trailing colon makes a zerodimensional view.
Construction
KeyedArray(rand(Int8, 2,10), ([:a, :b], 10:10:100)) # AbstractArray, Tuple{AbstractVector, ...}
A nested pair of wrappers can be constructed with keywords for names, and everything should work the same way in either order:
KeyedArray(rand(Int8, 2,10), row=[:a, :b], col=10:10:100) # KeyedArray(NamedDimsArray(...))
NamedDimsArray(rand(Int8, 2,10), row=[:a, :b], col=10:10:100) # NamedDimsArray(KeyedArray(...))
Calling AxisKeys.keyless(A)
removes the KeyedArray
wrapper, if any,
and NamedDims.unname(A)
similarly removes the names (regardless of which is outermost).
The function wrapdims
does a bit more checking and fixing, but is not typestable.
It will adjust the length of ranges of keys if it can,
and will fix indexing offsets if needed to match the array.
The resulting order of wrappers is controlled by AxisKeys.nameouter()=false
.
wrapdims(rand(Int8, 10), alpha='a':'z')
# Warning: range 'a':1:'z' replaced by 'a':1:'j', to match size(A, 1) == 10
wrapdims(OffsetArray(rand(Int8, 10),1), iter=10:10:100)
axiskeys(ans,1) # 10:10:100 with indices 0:9
Finally, wrapdims
will also convert AxisArray
s, NamedArray
s, as well as NamedTuple
s.
Functions
The function axes(A)
returns (a tuple of vectors of) indices as usual,
and axiskeys(A)
similarly returns (a tuple of vectors of) keys.
If the array has names, then dimnames(A)
returns them.
These functions work like size(A, d) = size(A, name)
to get just one.
The following things should work:

Broadcasting
log.(A)
andmap(log, A)
, as well as comprehensions[log(x) for x in A]
should all work. 
Transpose etc,
permutedims
,mapslices
. 
Concatenation
hcat(B, B .+ 100)
works. Note that the keys along the glued direction may not be unique afterwards. 
Reductions like
sum(A; dims=:channel)
can use dimension names. Likewiseprod
,mean
etc., anddropdims
. 
Sorting:
sortslices
permutes keys & data by the array, whilesortkeys
goes by the keys. 
Some linear algebra functions like
*
and\
will work. 
Getproperty returns the key vector, to allow things like
for (i,t) in enumerate(A.time); fun(val = A[i,:], time = t); ...
. 
Vectors support
push!(V, val)
, which will try to extend the key vector. There is also a methodpush!(V, key => val)
which pushes in a new key.
To allow for this limited mutability, V.keys isa Ref
for vectors,
while A.keys isa Tuple
for matrices & higher. But axiskeys(A)
always returns a tuple.

Named tuples can be converted to and from keyed vectors, with
collect(keys(nt)) == Symbol.(axiskeys(V),1)

FFTW
.fft
transforms the keys; if these are times such as Unitful.s
then the results are fequency labels. (PR#15.) 
LazyStack
.stack
understands names and keys. Stacks of named tuples likestack((a=i, b=i^2) for i=1:5)
create a matrix with[:a, :b]
. 
NamedPlus has a macro which works on comprehensions:
@named [n^pow for n=1:10, pow=0:2:4]
has names and keys.
Absent
 There is no automatic alignment of dimensions by name.
Thus
A .+ A[iter=3]
is fine as both names and keys line up, butA .+ B
is an error, asB
's first name is:time
not:channel
. (See NamedPlus.@named
for something like this.)
As for NamedDims.jl, the guiding idea is that every operation which could be done on ordinary arrays should still produce the same data, but propagate the extra information (names/keys), and error if it conflicts.
Both packages allow for wildcards, which never conflict.
In NamedDims.jl this is the name :_
, here it is a Base.OneTo(n)
,
like the axes
of an Array
. These can be constructed as
M = wrapdims(rand(2,2); _=[:a, :b], cols=nothing)
,
and for instance M .+ M'
is not an error.
 There are no special types provided for key vectors, they can be any
AbstractVector
s. Lookup happens by callingi = findfirst(isequal(20.0), axiskeys(A,2))
, oris = findall(<(18), axiskeys(A,2))
.
If you need lookup to be very fast, then you will want to use a package like
UniqueVectors.jl
or AcceleratedArrays.jl
or CategoricalArrays.jl.
To apply such a type to all dimensions, you may write
D = wrapdims(rand(1000), UniqueVector, rand(Int, 1000))
.
Then D(n)
here will use the fast lookup from UniqueVectors.jl (about 60x faster).
When a key vector is a Julia AbstractRange
, then this package provides some faster
overloads for things like findall(<=(42), 10:10:100)
.

There is also no automatic alignment by keys, like time. But this could be done elsewhere?

There is no interaction with interpolation, although this seems a natural fit. Why doesn't
A(:left, 13.7, :)
interpolate along continuous dimensions?
Elsewhere
This is more or less an attempt to replace AxisArrays
with several smaller packages. The complaints are:
(1) It's confusing to guess whether to perform indexing or lookup
based on whether it is given an integer (index) or not (key).
(2) Each "axis" was its own type Axis{:name}
which allowed zerooverhead lookup
before Julia 1.0. But this is now possible with a simpler design.
(They were called axes before Base.axes()
was added, hence (3) the confusing terminology.)
(4) Broadcasting is not supported, as this changed dramatically in Julia 1.0.
(5) There are lots of assorted functions, special categorical vector types, etc.
which aren't part of the core.
Other older packages (preJulia1.0):

NamedArrays also provides names & keys, which are always
OrderedDict
s. Named lookup looks likeNA[:x => 13.0]
instead ofA(x=13.0)
here; this is not very fast. Dimension names & keys can be set after creation. Has nice prettyprinting routines. Returned by FreqTables. 
LabelledArrays adds names for individual elements, more like a NamedTuple. Only for small sizes: the storage inside is a Tuple, not an Array.

AxisArrayPlots has some plot recipes.

OffsetArrays actually changes the indices of an Array, allowing any continuous integer range, like
0:9
or10:10
. This package is happy to wrap such arrays, and if needed will adjust indices of the given key vectors:O = wrapdims(OffsetArray(["left", "mid", "right"], 1:1), 'A':'C')
, thenO[1:0]
works.
Other new packages (post1.0):

Dictionaries does very fast lookup only (in this terminology), with no indexing. Not
<: AbstractArray
, not a wrapped around an Array. And presently only onedimensional. 
NamedPlus is some experiments using NamedDims. Function
align
permutes dimensions automatically, and macro@named
can introduce this into broadcasting expressions. 
DimensionalData is another replacement for AxisArrays. It again uses types like
Dim{:name}
to store both name & keys, plus some special ones likeX, Y
of the same abstract type (which must be in scope). Named lookup then looks likeDA[X < At(13.0)]
, roughly likeA(x=13.0)
here. 
AxisIndices differs mainly by storing the keys with the axes in its own
Axis
type. This is returned byBase.axes(A)
(instead ofBase.OneTo
etc.) like PR#6. Does not handle dimension names. (Grew out of the same discussion thread!) 
IndexedDims [in progress?] like this package adds keys on top of the names from NamedDims. These key vectors must always be AcceleratedArrays. Like AxisArrays, it tries to guess whether to do indexing or lookup based on type.
See also docs/speed.jl for some checks on this package, and comparisons to other ones. And see docs/repl.jl for some usage examples, showing pretty printing. For discussion, see AxisArraysFuture, and AxisArrays#84.
In

xarray does indexing
x[:, 0]
and lookup by "coordinate label" asx.loc[:, 'IA']
; with names these becomex.isel(space=0)
andda.sel(space='IA')
. 
pandas is really more like DataFrames, only one and twodimensional. Writes indexing "by position" as
df.iat[1, 1]
for scalars ordf.iloc[1:3, :]
allowing slices, and lookup "by label" asdf.at[dates[0], 'A']
for scalars ordf.loc['20130102':'20130104', ['A', 'B']]
for slices, "both endpoints are included" in this. See also Pandas.jl for a wrapper.